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Microbial biofilms are ubiquitous within porous media and the dynamics of their growth influence surface and subsurface flow patterns which impacts the physical properties of porous media and large-scale transport of solutes. A two-dimensional pore-scale numerical model was used to evaluate the impact of biofilm-induced flow heterogeneities on conservative transport. Our study integrates experimental biofilm images of Paenibacillus 300A strain in a microfluidic device packed with cylindrical grains in a hexagonal distribution, with mathematical modeling. Biofilm is represented as a synthetic porous structure with locally varying physical properties that honors the impact of biofilm on the porous medium. We find that biofilm plays a major role in shaping the observed conservative transport dynamics by enhancing anomalous characteristics. More specifically, when biofilm is present, the pore structure in our geometry becomes more spatially correlated. We observe intermittent behavior in the Lagrangian velocities that switches between fast transport periods and long trapping events. Our results suggest that intermittency enhances solute spreading in breakthrough curves which exhibit extreme anomalous slope at intermediate times and very marked late solute arrival due to solute retention. The efficiency of solute retention by the biofilm is controlled by a transport regime which can extend the tailing in the concentration breakthrough curves. These results indicate that solute retention by the biofilm exerts a strong control on conservative solute transport at pore-scale, a role that to date has not received enough attention.

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Porous materials are widely used in many heat transfer applications. Modeling porous materials at the microscopic level can accurately incorporate the detailed structure and substance parameters and thus provides valuable information for the complex heat transfer processes in such media. In this study, we use the generalized periodic boundary condition for pore-scale simulations of thermal flows in porous materials. A two-dimensional porous model consisting of circular solid domains is considered, and comprehensive simulations are performed to study the influences on macroscopic thermal conductivity from several microscopic system parameters, including the porosity, Reynolds number, and periodic unit aspect ratio and the thermal conductance at the solid-fluid interface. Our results show that, even at the same porosity and Reynolds number, the aspect ratio of the periodic unit and the interfacial thermal conductance can significantly affect the macroscopic thermal behaviors of porous materials. Qualitative analysis is also provided to relate the apparent thermal conductivity to the complex flow and temperature distributions in the microscopic porous structure. The method, findings and discussions presented in this paper could be useful for fundamental studies, material development, and engineering applications of porous thermal flow systems.

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Fluids exhibiting non-Newtonian rheologies are used in a range of applications, including hydraulic fracturing, enhanced oil recovery, remediation, and industrial processes. Hydraulic fracturing in particular has received attention from environmental scientists, policy-makers, and the general public due in part to concerns about the possibility of contamination of groundwater resources by the complex and potentially harmful fluids used in the process. The non-Newtonian nature of many hydraulic fracturing fluids complicates the prediction of their movement, and precludes use of most traditional flow and transport models. To improve understanding of the flow of such fluids in porous media, a series of column experiments was conducted and a pore-scale lattice Boltzmann model (LBM) was developed, verified, and used to simulate analogous systems. Flow experiments were conducted with guar gum solutions of varying concentration and three porous media systems. The LBM was developed for transient, three-dimensional porous medium systems and included a shear rate-dependent dynamic viscosity based on the Cross rheological model. The LBM was verified using a semi-analytical solution for Cross model fluid flow, OpenFOAM simulations, and grid resolution inter-comparisons between two different solution approaches. Simulations were performed on synthetic porous medium systems produced with a sphere packing algorithm to approximate the properties of the experimental systems. The simulations were in good agreement with the experimental results, particularly for systems that exhibited the greatest non-Newtonian character. The modeling approach developed in this work provides a valuable tool for investigating relationships between pore-scale fluid flow and macroscale variables of interest for simulating movement of non-Newtonian fluids at larger scales.

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Microbial communities in agricultural soils underpin many ecosystem services including the maintenance of soil structure, food production, water purification and carbon storage. However, the impact of fertilization on the health of microbial communities is not well understood. This study investigates the spatial and temporal dynamics of nitrogen (N) transport away from a fertilizer granule with pore scale resolution. Specifically, we examined how soil structure and moisture content influence fertilizer derived N movement through the soil pore network and the subsequent impact of on soil microbial communities. We develop a mathematical model to describe N transport and reactions in soil at the pore-scale. Using X-ray Computed Tomography scans, we reconstructed a microscale description of a soil-pore geometry as a computational mesh. Solving two-phase water/air model produced pore-scale water distributions at 15, 30 and 70% water-filled pore volume. The N-speciation model considered ammonium (NH4+), nitrate (NO3-) and dissolved organic N (DON), and included N immobilization, ammonification and nitrification processes, as well as diffusion in soil solution. We simulated the dissolution of a fertilizer pellet and a pore scale N cycle at three different water saturations. To aid interpretation of the model results, microbial activity at a range of N concentrations was measured. The model showed that the diffusion and concentration of N in water films is critically dependent upon soil moisture and N species. We predict that the maximum NH4+ and NO3- concentrations in soil solution around the pellet under dry conditions are in the order of 1 × 103 and 1 × 104 mol m-3 respectively, and under wet conditions 2 × 102 and 1 × 103 mol m-3, respectively. Supporting experimental evidence suggests that these concentrations would be sufficient to reduce microbial activity in the short-term in the zone immediately around the fertilizer pellet (ranging from 0.9 to 3.8 mm), causing a major loss of soil biological functioning. This model demonstrates the importance of pore-scale processes in regulating N movement and their interactions with the soil microbiome.

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Mass transfer in porous media resulting from dispersion occurs in a wide variety of applications such as water treatment, flow batteries, flow in aquifers, enhanced oil recovery, and packed-bed reactors. The underlying mechanisms of dispersion are the molecular diffusion superimposed on the advective transport induced by the fluid flow. Modeling dispersion in pore networks can be performed at a much lower computational cost compared to that in direct numerical simulations (DNS) such as finite element or the lattice Boltzmann methods, so it can be regarded as a suitable alternative provided its accuracy is sufficient. The most common approach to model dispersion in network models is based on the first-order upwind scheme, despite its known limitations in terms of accuracy for certain flow and transport regimes. In this study, three alternative pore-scale models for dispersion, which are more accurate than the existing ones, were derived and tested in pore network simulations. These models were adopted from the CFD literature and are based on a spatial discretization of the advection-diffusion equation using the hybrid and power-law finite difference schemes and the exact solution of the one-dimensional advection-diffusion equation. Finally, considering dispersion problems over arbitrary porous structures, consisting of stick-and-ball geometries, and different flow and mass transfer arrangements, the developed models were validated. Validation was carried-out through comparisons between results obtained with DNS, using a finite element solver, and those from pore network simulations. It is shown that under a wide range of dispersion regimes (up to the onset of the dispersion power-law regime), the relative error (with respect to DNS results) introduced by the power-law and exact solution-based models is consistently below 1%, whereas the use of the upwind scheme leads to >10% of relative error, depending on the dispersion regime. All the dispersion models developed in this study were implemented as part of the open-source network modeling package, OpenPNM.

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The mobilization mechanism of the trapped phases controlled by the viscous force and capillary force in porous media is crucial to various engineering applications. In this paper, pore scale water flooding process in rock models with nonuniform wettability is simulated by computational fluid dynamics (CFD) using the volume of fluid (VOF) model. Four types of rock are imaged by micro-CT (µ-CT) and adopted as inputs to generate the structured mesh models. The simulations of two-phase flow are carried out to study the immiscible displacement process in the development of oil fields. The scaling-up critical capillary number at micro-macro scale are acquired and validated, the effects of which on relative permeability, residual oil recovery and immiscible displacement efficiency are analyzed. The simulation results indicate that the critical capillary number at microscopic scale ranges from 10-6 to 10-5 for water-wetted and oil-wetted rock respectively, and approaches to 1 at the macro scale. The effect of wettability on oil recovery is positive for intermediate-wetted or weak water-wetted rock, while negative for strong wettability.

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Coated paper is an example of a multi-layer porous medium, involving a coating layer along the two surfaces of the paper and a fibrous layer in the interior of the paper. The interface between these two media needs to be characterized in order to develop relevant modeling tools. After careful cutting of the paper, a cross section was imaged using focused ion beam scanning electron microscopy. The resulting image was analyzed to characterize the coating layer and its transition to the fibrous layer. Such image analysis showed that the coating layer thickness is highly variable, with a significant fraction of it being thinner than a minimum thickness required to keep ink from invading into the fibrous layer. The overall structure of the coating and fibrous layers observed in this analysis provide insights into how the system should be modeled, with the resulting conclusion pointing to a specific kind of multi-scale modeling approach.

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Surface charge at solid-electrolyte interface is generally coupled with the local electrolyte properties (ionic concentration, pH, etc.), and therefore not as assumed homogeneous on the solid surfaces in the previous studies. The inhomogeneous charge brings huge challenges in predictions of electro-osmotic transport and has never been well studied. In this work, we first propose a classification of electro-osmosis based on a dimensionless number which is the ratio of the Debye length to the characteristic pore size. In the limit of thin electrical double layer, we establish a pore-scale numerical model for inhomogeneously charged electro-osmosis including four ions: Na+,Cl-,H+ and OH-. Based on reconstructed porous media, we simulate the electro-osmosis with inhomogeneous charge using lattice Boltzmann method. The nonlinear response of electro-osmotic velocity to applied electrical field and the reverse flow have been observed and analyzed.

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In this study, uncoated paper was characterized. Three-dimensional structure of the layer was reconstructed using imaging results of micro-CT scanning with a relatively high resolution ( 0.9 µ m ) . Image analysis provided the pore space of the layer, which was used to determine its porosity and pore size distribution. Representative elementary volume (REV) size was determined by calculating values of porosity and permeability values for varying domain sizes. We found that those values remained unchanged for domain sizes of 400 × 400 × 150 µ m 3 and larger; this was chosen as the REV size. The determined REV size was verified by determining capillary pressure-saturation imbibition curves for various domain sizes. We studied the directional dependence of curves by simulating water penetration into the layer from various directions. We did not find any significant difference between curves in different directions. We studied the effect of compression of paper on curves. We found that up to 30% compression of the paper layer had very small effect on the curve. Relative permeability as a function of saturation was also calculated. Water penetration into paper was visualized using confocal laser scanning microscopy. Dynamic visualization of water flow in the paper showed that water moves along the fibers first and then fills the pores between them.

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We compare the ability of various continuum-scale models to reproduce the key features of a transport setting associated with a bimolecular reaction taking place in the fluid phase and numerically simulated at the pore-scale level in a disordered porous medium. We start by considering a continuum-scale formulation which results from formal upscaling of this reactive transport process by means of volume averaging. The resulting (upscaled) continuum-scale system of equations includes nonlocal integro-differential terms and the effective parameters embedded in the model are quantified directly through computed pore-scale fluid velocity and pore space geometry attributes. The results obtained through this predictive model formulation are then compared against those provided by available effective continuum models which require calibration through parameter estimation. Our analysis considers two models recently proposed in the literature which are designed to embed incomplete mixing arising from the presence of fast reactions under advection-dominated transport conditions. We show that best estimates of the parameters of these two models heavily depend on the type of data employed for model calibration. Our upscaled nonlocal formulation enables us to reproduce most of the critical features observed through pore-scale simulation without any model calibration. As such, our results clearly show that embedding into a continuum-scale model the information content associated with pore-scale geometrical features and fluid velocity yields improved interpretation of typically available continuum-scale transport observations.

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